12n
0619
(K12n
0619
)
A knot diagram
1
Linearized knot diagam
3 8 6 11 9 1 11 2 4 7 9 4
Solving Sequence
3,8
2 9
1,11
7 6 4 5 10 12
c
2
c
8
c
1
c
7
c
6
c
3
c
4
c
10
c
12
c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.28036 × 10
89
u
71
+ 6.03330 × 10
89
u
70
+ ··· + 9.62134 × 10
90
b + 1.51309 × 10
91
,
2.28885 × 10
91
u
71
− 3.14485 × 10
90
u
70
+ ··· + 1.25077 × 10
92
a − 5.93546 × 10
92
, u
72
+ u
71
+ ··· − 5u + 13i
I
u
2
= h58306u
29
− 92181u
28
+ ··· + 145157b − 132553,
213726u
29
− 58787u
28
+ ··· + 145157a − 315469, u
30
+ 8u
28
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 102 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h4.28 × 10
89
u
71
+ 6.03 × 10
89
u
70
+ · · · + 9.62 × 10
90
b + 1.51 × 10
91
, 2.29 ×
10
91
u
71
−3.14×10
90
u
70
+· · ·+1.25×10
92
a−5.94×10
92
, u
72
+u
71
+· · ·−5u+13i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
−0.182994u
71
+ 0.0251433u
70
+ ··· − 18.8680u + 4.74543
−0.0444882u
71
− 0.0627074u
70
+ ··· + 7.89374u − 1.57263
a
7
=
−0.133370u
71
+ 0.0680367u
70
+ ··· − 7.84939u − 3.40355
−0.00317815u
71
+ 0.0974739u
70
+ ··· − 5.89041u + 5.78176
a
6
=
−0.150162u
71
+ 0.195372u
70
+ ··· − 15.9473u + 1.82218
−0.0760366u
71
+ 0.0252163u
70
+ ··· − 5.90165u + 3.91591
a
4
=
0.453018u
71
+ 0.167249u
70
+ ··· + 12.8155u − 3.75646
0.215863u
71
+ 0.311273u
70
+ ··· − 4.36625u + 4.19897
a
5
=
0.188422u
71
− 0.0605806u
70
+ ··· + 12.5787u + 0.355877
−0.0375701u
71
+ 0.0536453u
70
+ ··· + 2.51828u − 2.99277
a
10
=
−0.580665u
71
− 0.174180u
70
+ ··· − 9.44693u + 5.13081
−0.225939u
71
− 0.372106u
70
+ ··· + 10.8961u − 6.94834
a
12
=
−0.215107u
71
− 0.0246516u
70
+ ··· − 19.2815u + 5.20660
−0.0206372u
71
− 0.0874849u
70
+ ··· + 7.80928u − 0.881593
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.23866u
71
+ 1.66942u
70
+ ··· + 6.74520u + 28.1649
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 29u
71
+ ··· + 1483u + 169
c
2
, c
8
u
72
+ u
71
+ ··· − 5u + 13
c
3
u
72
− 8u
71
+ ··· − 1454u + 103
c
4
u
72
− 2u
71
+ ··· + 2563738u + 372821
c
5
u
72
− 6u
71
+ ··· − 62302304u + 12968512
c
6
u
72
+ 2u
71
+ ··· − 81136u + 4448
c
7
, c
10
u
72
− 3u
71
+ ··· − 11u − 1
c
9
u
72
+ u
71
+ ··· − 77411u − 34673
c
11
u
72
+ 7u
71
+ ··· − 7376u − 2363
c
12
u
72
+ 10u
71
+ ··· − 582696u − 825103
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
+ 41y
71
+ ··· − 4031249y + 28561
c
2
, c
8
y
72
+ 29y
71
+ ··· + 1483y + 169
c
3
y
72
+ 8y
71
+ ··· + 86788y + 10609
c
4
y
72
− 108y
71
+ ··· − 1786672638490y + 138995498041
c
5
y
72
− 78y
71
+ ··· + 6347781005638656y + 168182303494144
c
6
y
72
+ 24y
71
+ ··· − 1766542592y + 19784704
c
7
, c
10
y
72
− 63y
71
+ ··· + 91y + 1
c
9
y
72
− 99y
71
+ ··· − 7903121y + 1202216929
c
11
y
72
− 105y
71
+ ··· − 197872558y + 5583769
c
12
y
72
− 56y
71
+ ··· − 78126375735346y + 680794960609
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.808887 + 0.575194I
a = −0.684141 − 1.018880I
b = −1.59723 + 0.99383I
4.62016 + 3.05851I 0
u = −0.808887 − 0.575194I
a = −0.684141 + 1.018880I
b = −1.59723 − 0.99383I
4.62016 − 3.05851I 0
u = −0.696036 + 0.740230I
a = −0.037316 − 0.349653I
b = 1.31015 + 0.85715I
6.64464 − 3.46257I 0
u = −0.696036 − 0.740230I
a = −0.037316 + 0.349653I
b = 1.31015 − 0.85715I
6.64464 + 3.46257I 0
u = −0.507319 + 0.820349I
a = −1.222130 + 0.637102I
b = −0.580847 + 0.867836I
−3.86547 − 2.02217I 6.00000 + 0.I
u = −0.507319 − 0.820349I
a = −1.222130 − 0.637102I
b = −0.580847 − 0.867836I
−3.86547 + 2.02217I 6.00000 + 0.I
u = −0.116021 + 0.940603I
a = 0.784994 − 0.355068I
b = 0.65806 + 1.54944I
2.64894 − 3.41631I 3.10260 + 2.08330I
u = −0.116021 − 0.940603I
a = 0.784994 + 0.355068I
b = 0.65806 − 1.54944I
2.64894 + 3.41631I 3.10260 − 2.08330I
u = 0.673339 + 0.666930I
a = −1.09226 + 1.19514I
b = −0.87160 − 1.61399I
11.74130 + 0.35138I 18.3982 + 2.1314I
u = 0.673339 − 0.666930I
a = −1.09226 − 1.19514I
b = −0.87160 + 1.61399I
11.74130 − 0.35138I 18.3982 − 2.1314I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814321 + 0.703037I
a = 0.89240 + 1.61244I
b = 1.70285 − 0.14650I
13.40880 + 1.35348I 0
u = −0.814321 − 0.703037I
a = 0.89240 − 1.61244I
b = 1.70285 + 0.14650I
13.40880 − 1.35348I 0
u = 0.163802 + 1.063820I
a = −0.618870 + 0.559588I
b = −1.035320 − 0.100786I
−2.41601 + 2.16254I 0
u = 0.163802 − 1.063820I
a = −0.618870 − 0.559588I
b = −1.035320 + 0.100786I
−2.41601 − 2.16254I 0
u = 0.082091 + 1.074760I
a = 0.393708 − 1.225530I
b = 0.041526 − 1.307790I
7.12176 + 1.27412I 0
u = 0.082091 − 1.074760I
a = 0.393708 + 1.225530I
b = 0.041526 + 1.307790I
7.12176 − 1.27412I 0
u = −0.381326 + 0.829948I
a = 1.264630 − 0.364539I
b = 0.22348 − 1.40162I
−4.56914 − 1.60830I 11.92985 + 7.22454I
u = −0.381326 − 0.829948I
a = 1.264630 + 0.364539I
b = 0.22348 + 1.40162I
−4.56914 + 1.60830I 11.92985 − 7.22454I
u = 0.727539 + 0.822056I
a = −1.044260 + 0.906641I
b = −2.41732 − 0.54518I
4.49876 − 0.62881I 0
u = 0.727539 − 0.822056I
a = −1.044260 − 0.906641I
b = −2.41732 + 0.54518I
4.49876 + 0.62881I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.787450 + 0.775531I
a = −0.77260 − 1.30907I
b = −0.086400 − 1.042150I
8.46954 − 2.16031I 0
u = 0.787450 − 0.775531I
a = −0.77260 + 1.30907I
b = −0.086400 + 1.042150I
8.46954 + 2.16031I 0
u = −0.707731 + 0.849293I
a = −0.453970 − 1.024470I
b = −1.43457 + 0.83997I
4.40743 − 0.27804I 0
u = −0.707731 − 0.849293I
a = −0.453970 + 1.024470I
b = −1.43457 − 0.83997I
4.40743 + 0.27804I 0
u = −0.703670 + 0.875856I
a = 0.974104 + 0.503213I
b = 2.34182 − 0.65068I
4.32813 − 5.13090I 0
u = −0.703670 − 0.875856I
a = 0.974104 − 0.503213I
b = 2.34182 + 0.65068I
4.32813 + 5.13090I 0
u = 0.909432 + 0.660037I
a = 1.199680 − 0.671979I
b = 1.87323 + 0.59826I
5.55068 − 0.89067I 0
u = 0.909432 − 0.660037I
a = 1.199680 + 0.671979I
b = 1.87323 − 0.59826I
5.55068 + 0.89067I 0
u = 0.638035 + 0.594328I
a = 0.489358 + 0.549201I
b = 0.153674 + 0.397027I
1.46159 + 0.94369I 8.05381 − 3.32759I
u = 0.638035 − 0.594328I
a = 0.489358 − 0.549201I
b = 0.153674 − 0.397027I
1.46159 − 0.94369I 8.05381 + 3.32759I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.292414 + 1.099760I
a = −0.045977 + 0.161008I
b = −0.183182 − 0.301441I
−3.74250 − 0.35528I 0
u = −0.292414 − 1.099760I
a = −0.045977 − 0.161008I
b = −0.183182 + 0.301441I
−3.74250 + 0.35528I 0
u = 0.711303 + 0.912423I
a = 0.868327 − 1.090420I
b = 2.09993 + 0.93166I
4.21886 + 6.12406I 0
u = 0.711303 − 0.912423I
a = 0.868327 + 1.090420I
b = 2.09993 − 0.93166I
4.21886 − 6.12406I 0
u = 0.594374 + 1.009220I
a = 0.509259 + 0.475060I
b = 0.236822 + 0.688574I
0.20929 + 3.90599I 0
u = 0.594374 − 1.009220I
a = 0.509259 − 0.475060I
b = 0.236822 − 0.688574I
0.20929 − 3.90599I 0
u = 0.034956 + 0.821119I
a = −0.41604 − 1.41541I
b = −0.161306 + 0.517047I
0.25599 − 2.44516I 3.51232 + 3.05197I
u = 0.034956 − 0.821119I
a = −0.41604 + 1.41541I
b = −0.161306 − 0.517047I
0.25599 + 2.44516I 3.51232 − 3.05197I
u = −1.013690 + 0.601362I
a = 0.99520 + 1.11698I
b = 1.73415 − 0.41392I
15.2060 + 9.6384I 0
u = −1.013690 − 0.601362I
a = 0.99520 − 1.11698I
b = 1.73415 + 0.41392I
15.2060 − 9.6384I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.677870 + 0.977881I
a = 0.213548 − 0.199030I
b = 0.580098 + 1.130410I
5.90968 − 1.84580I 0
u = −0.677870 − 0.977881I
a = 0.213548 + 0.199030I
b = 0.580098 − 1.130410I
5.90968 + 1.84580I 0
u = 0.655258 + 1.004640I
a = 0.723304 − 0.915460I
b = 2.78885 − 0.55758I
10.71060 + 4.84302I 0
u = 0.655258 − 1.004640I
a = 0.723304 + 0.915460I
b = 2.78885 + 0.55758I
10.71060 − 4.84302I 0
u = 0.738710 + 0.963164I
a = −1.19204 − 0.78105I
b = −0.675198 − 1.198490I
7.89130 + 7.92115I 0
u = 0.738710 − 0.963164I
a = −1.19204 + 0.78105I
b = −0.675198 + 1.198490I
7.89130 − 7.92115I 0
u = 1.144690 + 0.425981I
a = −1.218740 + 0.443843I
b = −1.52526 − 0.51644I
13.72910 + 2.93341I 0
u = 1.144690 − 0.425981I
a = −1.218740 − 0.443843I
b = −1.52526 + 0.51644I
13.72910 − 2.93341I 0
u = −0.550235 + 1.099390I
a = −0.0754485 + 0.0197779I
b = 0.160032 − 0.367219I
−1.98390 − 7.01272I 0
u = −0.550235 − 1.099390I
a = −0.0754485 − 0.0197779I
b = 0.160032 + 0.367219I
−1.98390 + 7.01272I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731363 + 1.014090I
a = −1.37318 − 0.69630I
b = −2.48364 + 0.63785I
12.4616 − 7.1678I 0
u = −0.731363 − 1.014090I
a = −1.37318 + 0.69630I
b = −2.48364 − 0.63785I
12.4616 + 7.1678I 0
u = −0.697806 + 1.047480I
a = 0.861122 + 0.565843I
b = 2.63010 − 0.99051I
3.25158 − 8.71682I 0
u = −0.697806 − 1.047480I
a = 0.861122 − 0.565843I
b = 2.63010 + 0.99051I
3.25158 + 8.71682I 0
u = −0.655934 + 0.321949I
a = 0.195232 + 0.043457I
b = −0.292662 + 0.217665I
0.19630 + 2.31331I 2.50410 − 3.87759I
u = −0.655934 − 0.321949I
a = 0.195232 − 0.043457I
b = −0.292662 − 0.217665I
0.19630 − 2.31331I 2.50410 + 3.87759I
u = 0.764755 + 1.056800I
a = −0.768111 + 0.967366I
b = −2.03014 − 0.43609I
4.34565 + 7.06034I 0
u = 0.764755 − 1.056800I
a = −0.768111 − 0.967366I
b = −2.03014 + 0.43609I
4.34565 − 7.06034I 0
u = −0.078514 + 0.637068I
a = −0.140949 + 1.209800I
b = −0.473595 + 1.195070I
0.91968 + 2.40413I −0.54237 − 2.15079I
u = −0.078514 − 0.637068I
a = −0.140949 − 1.209800I
b = −0.473595 − 1.195070I
0.91968 − 2.40413I −0.54237 + 2.15079I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.764358 + 1.130520I
a = −1.077160 − 0.723013I
b = −2.58282 + 0.58816I
13.5431 − 16.0927I 0
u = −0.764358 − 1.130520I
a = −1.077160 + 0.723013I
b = −2.58282 − 0.58816I
13.5431 + 16.0927I 0
u = −0.027747 + 1.400220I
a = −0.174463 + 0.765705I
b = −0.608195 − 0.323463I
−2.16290 + 0.96975I 0
u = −0.027747 − 1.400220I
a = −0.174463 − 0.765705I
b = −0.608195 + 0.323463I
−2.16290 − 0.96975I 0
u = 0.157578 + 1.394680I
a = 0.323172 − 0.990570I
b = 0.505882 − 0.267746I
6.98353 + 7.23116I 0
u = 0.157578 − 1.394680I
a = 0.323172 + 0.990570I
b = 0.505882 + 0.267746I
6.98353 − 7.23116I 0
u = 0.77726 + 1.28992I
a = 0.610495 − 0.781522I
b = 1.87938 + 0.13816I
11.07580 + 3.96205I 0
u = 0.77726 − 1.28992I
a = 0.610495 + 0.781522I
b = 1.87938 − 0.13816I
11.07580 − 3.96205I 0
u = −0.203804 + 0.401097I
a = 0.29924 − 1.98542I
b = 0.28052 + 2.03618I
4.74098 + 2.25423I 11.54945 − 5.18126I
u = −0.203804 − 0.401097I
a = 0.29924 + 1.98542I
b = 0.28052 − 2.03618I
4.74098 − 2.25423I 11.54945 + 5.18126I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444431
a = 1.32156
b = 0.457135
0.813147 12.3290
u = 0.292517
a = −5.77870
b = 0.220364
10.8708 3.55680
12
II. I
u
2
= h58306u
29
− 92181u
28
+ · · · + 145157b − 132553, 2.14 × 10
5
u
29
−
5.88 × 10
4
u
28
+ · · · + 1.45 × 10
5
a − 3.15 × 10
5
, u
30
+ 8u
28
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
−1.47238u
29
+ 0.404989u
28
+ ··· − 12.9692u + 2.17330
−0.401675u
29
+ 0.635043u
28
+ ··· − 6.12894u + 0.913170
a
7
=
2.01653u
29
− 0.240560u
28
+ ··· + 10.3514u − 0.616808
0.712808u
29
+ 0.388531u
28
+ ··· + 1.99596u + 0.773955
a
6
=
2.55462u
29
+ 0.167591u
28
+ ··· + 14.9088u − 1.00973
0.174852u
29
+ 0.258892u
28
+ ··· + 1.99550u + 0.236165
a
4
=
1.70447u
29
− 0.769353u
28
+ ··· + 14.5271u − 5.00674
0.230351u
29
− 1.65192u
28
+ ··· + 5.14174u − 2.38759
a
5
=
2.31155u
29
− 0.307440u
28
+ ··· + 13.6258u − 0.778295
0.377440u
29
+ 0.00674442u
28
+ ··· + 0.00549750u + 0.942635
a
10
=
1.03500u
29
+ 1.30748u
28
+ ··· − 3.08951u + 2.26109
0.186770u
29
− 0.118678u
28
+ ··· + 0.707145u − 0.350117
a
12
=
−2.01033u
29
+ 0.275350u
28
+ ··· − 12.9696u + 1.63551
−0.889272u
29
+ 0.343531u
28
+ ··· − 5.85073u + 0.505019
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1400610
145157
u
29
+
939828
145157
u
28
+ ··· +
3223212
145157
u +
2462379
145157
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
30
− 16u
29
+ ··· − 18u + 1
c
2
u
30
+ 8u
28
+ ··· − 2u + 1
c
3
u
30
− 11u
29
+ ··· − 3u + 1
c
4
u
30
+ u
29
+ ··· + 25u + 13
c
5
u
30
+ 3u
29
+ ··· − 104u + 16
c
6
u
30
− u
29
+ ··· − 84u + 8
c
7
u
30
− 2u
29
+ ··· − 2u + 1
c
8
u
30
+ 8u
28
+ ··· + 2u + 1
c
9
u
30
− 8u
28
+ ··· − 4u + 1
c
10
u
30
+ 2u
29
+ ··· + 2u + 1
c
11
u
30
− 14u
29
+ ··· − 599u + 77
c
12
u
30
− 5u
29
+ ··· − u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 8y
29
+ ··· − 54y + 1
c
2
, c
8
y
30
+ 16y
29
+ ··· + 18y + 1
c
3
y
30
− 5y
29
+ ··· − 9y + 1
c
4
y
30
− 21y
29
+ ··· + 1533y + 169
c
5
y
30
− 23y
29
+ ··· − 3520y + 256
c
6
y
30
− y
29
+ ··· − 1104y + 64
c
7
, c
10
y
30
− 16y
29
+ ··· − 18y + 1
c
9
y
30
− 16y
29
+ ··· + 10y + 1
c
11
y
30
− 38y
29
+ ··· − 117791y + 5929
c
12
y
30
− 13y
29
+ ··· + 17y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783418 + 0.632894I
a = −0.810991 − 1.018060I
b = −1.83940 + 0.78866I
3.40622 + 3.06203I 7.45974 − 2.51576I
u = −0.783418 − 0.632894I
a = −0.810991 + 1.018060I
b = −1.83940 − 0.78866I
3.40622 − 3.06203I 7.45974 + 2.51576I
u = 0.619760 + 0.865626I
a = 1.16399 + 0.94071I
b = 0.309140 + 1.239140I
−3.19194 + 2.43189I 12.01531 − 5.52437I
u = 0.619760 − 0.865626I
a = 1.16399 − 0.94071I
b = 0.309140 − 1.239140I
−3.19194 − 2.43189I 12.01531 + 5.52437I
u = −0.368581 + 1.000170I
a = −0.426345 − 0.302191I
b = 0.67189 + 1.63285I
3.60668 − 4.39482I 9.00853 + 6.46321I
u = −0.368581 − 1.000170I
a = −0.426345 + 0.302191I
b = 0.67189 − 1.63285I
3.60668 + 4.39482I 9.00853 − 6.46321I
u = 0.332552 + 0.864602I
a = −1.206910 − 0.245260I
b = −0.413045 − 1.160100I
−4.89037 + 1.43366I −8.45611 + 3.24752I
u = 0.332552 − 0.864602I
a = −1.206910 + 0.245260I
b = −0.413045 + 1.160100I
−4.89037 − 1.43366I −8.45611 − 3.24752I
u = −0.684283 + 0.854673I
a = 0.818321 + 0.115887I
b = 2.27305 + 0.07664I
6.45076 − 4.59120I 11.56923 + 7.10771I
u = −0.684283 − 0.854673I
a = 0.818321 − 0.115887I
b = 2.27305 − 0.07664I
6.45076 + 4.59120I 11.56923 − 7.10771I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335307 + 0.788308I
a = −0.308397 + 0.642481I
b = 0.30926 + 2.50864I
4.40509 + 1.42170I 7.66101 + 2.26727I
u = −0.335307 − 0.788308I
a = −0.308397 − 0.642481I
b = 0.30926 − 2.50864I
4.40509 − 1.42170I 7.66101 − 2.26727I
u = −0.725614 + 0.892152I
a = −0.091508 − 0.819126I
b = −0.476611 + 1.081330I
6.34146 − 0.80394I 13.14765 − 1.03633I
u = −0.725614 − 0.892152I
a = −0.091508 + 0.819126I
b = −0.476611 − 1.081330I
6.34146 + 0.80394I 13.14765 + 1.03633I
u = 0.582986 + 0.610428I
a = −1.23889 + 1.49928I
b = −0.75129 − 1.21355I
11.28510 + 0.73508I 7.51796 − 7.30910I
u = 0.582986 − 0.610428I
a = −1.23889 − 1.49928I
b = −0.75129 + 1.21355I
11.28510 − 0.73508I 7.51796 + 7.30910I
u = 0.255399 + 1.222230I
a = −0.324792 + 0.567201I
b = −0.847986 + 0.110219I
−3.30623 + 1.15332I 4.33144 − 1.27674I
u = 0.255399 − 1.222230I
a = −0.324792 − 0.567201I
b = −0.847986 − 0.110219I
−3.30623 − 1.15332I 4.33144 + 1.27674I
u = 0.540675 + 1.125620I
a = −0.222231 + 0.444877I
b = −0.534770 + 0.403381I
−1.49594 + 7.00148I 12.8281 − 7.0248I
u = 0.540675 − 1.125620I
a = −0.222231 − 0.444877I
b = −0.534770 − 0.403381I
−1.49594 − 7.00148I 12.8281 + 7.0248I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.700718 + 1.037000I
a = 0.874088 + 0.682487I
b = 2.43000 − 0.94490I
2.19546 − 8.69208I 4.75207 + 7.00700I
u = −0.700718 − 1.037000I
a = 0.874088 − 0.682487I
b = 2.43000 + 0.94490I
2.19546 + 8.69208I 4.75207 − 7.00700I
u = 0.711976 + 0.189161I
a = 1.061860 − 0.269522I
b = 0.438542 − 0.183348I
1.04863 − 2.30351I 12.72741 + 3.19180I
u = 0.711976 − 0.189161I
a = 1.061860 + 0.269522I
b = 0.438542 + 0.183348I
1.04863 + 2.30351I 12.72741 − 3.19180I
u = 0.640934 + 1.118050I
a = 0.700059 − 0.901785I
b = 2.11090 − 0.28974I
9.61448 + 4.20198I 7.63729 − 2.59179I
u = 0.640934 − 1.118050I
a = 0.700059 + 0.901785I
b = 2.11090 + 0.28974I
9.61448 − 4.20198I 7.63729 + 2.59179I
u = −0.127172 + 1.326790I
a = −0.146586 + 0.798852I
b = −0.384493 − 0.315318I
−2.41141 + 1.33974I 3.46635 − 9.18297I
u = −0.127172 − 1.326790I
a = −0.146586 − 0.798852I
b = −0.384493 + 0.315318I
−2.41141 − 1.33974I 3.46635 + 9.18297I
u = 0.040810 + 0.418157I
a = −0.34166 − 2.28175I
b = −0.295186 − 0.743488I
1.48560 − 2.52463I 14.3340 + 4.6539I
u = 0.040810 − 0.418157I
a = −0.34166 + 2.28175I
b = −0.295186 + 0.743488I
1.48560 + 2.52463I 14.3340 − 4.6539I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 16u
29
+ ··· − 18u + 1)(u
72
+ 29u
71
+ ··· + 1483u + 169)
c
2
(u
30
+ 8u
28
+ ··· − 2u + 1)(u
72
+ u
71
+ ··· − 5u + 13)
c
3
(u
30
− 11u
29
+ ··· − 3u + 1)(u
72
− 8u
71
+ ··· − 1454u + 103)
c
4
(u
30
+ u
29
+ ··· + 25u + 13)(u
72
− 2u
71
+ ··· + 2563738u + 372821)
c
5
(u
30
+ 3u
29
+ ··· − 104u + 16)
· (u
72
− 6u
71
+ ··· − 62302304u + 12968512)
c
6
(u
30
− u
29
+ ··· − 84u + 8)(u
72
+ 2u
71
+ ··· − 81136u + 4448)
c
7
(u
30
− 2u
29
+ ··· − 2u + 1)(u
72
− 3u
71
+ ··· − 11u − 1)
c
8
(u
30
+ 8u
28
+ ··· + 2u + 1)(u
72
+ u
71
+ ··· − 5u + 13)
c
9
(u
30
− 8u
28
+ ··· − 4u + 1)(u
72
+ u
71
+ ··· − 77411u − 34673)
c
10
(u
30
+ 2u
29
+ ··· + 2u + 1)(u
72
− 3u
71
+ ··· − 11u − 1)
c
11
(u
30
− 14u
29
+ ··· − 599u + 77)(u
72
+ 7u
71
+ ··· − 7376u − 2363)
c
12
(u
30
− 5u
29
+ ··· − u + 1)(u
72
+ 10u
71
+ ··· − 582696u − 825103)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 8y
29
+ ··· − 54y + 1)(y
72
+ 41y
71
+ ··· − 4031249y + 28561)
c
2
, c
8
(y
30
+ 16y
29
+ ··· + 18y + 1)(y
72
+ 29y
71
+ ··· + 1483y + 169)
c
3
(y
30
− 5y
29
+ ··· − 9y + 1)(y
72
+ 8y
71
+ ··· + 86788y + 10609)
c
4
(y
30
− 21y
29
+ ··· + 1533y + 169)
· (y
72
− 108y
71
+ ··· − 1786672638490y + 138995498041)
c
5
(y
30
− 23y
29
+ ··· − 3520y + 256)
· (y
72
− 78y
71
+ ··· + 6347781005638656y + 168182303494144)
c
6
(y
30
− y
29
+ ··· − 1104y + 64)
· (y
72
+ 24y
71
+ ··· − 1766542592y + 19784704)
c
7
, c
10
(y
30
− 16y
29
+ ··· − 18y + 1)(y
72
− 63y
71
+ ··· + 91y + 1)
c
9
(y
30
− 16y
29
+ ··· + 10y + 1)
· (y
72
− 99y
71
+ ··· − 7903121y + 1202216929)
c
11
(y
30
− 38y
29
+ ··· − 117791y + 5929)
· (y
72
− 105y
71
+ ··· − 197872558y + 5583769)
c
12
(y
30
− 13y
29
+ ··· + 17y + 1)
· (y
72
− 56y
71
+ ··· − 78126375735346y + 680794960609)
22
